We will describe the geometry of a smooth functorial compactification of the strata. That is, we will describe a compact algebraic variety that parameterizes the data of certain geometric multi-scale differentials, which compactifies the locus of smooth Riemann surfaces together with a differential with prescribed zeroes and poles. The multi-scale differentials are certain collections of meromorphic differentials on the components of nodal Riemann surfaces, together with some extra data. We will describe the general construction and define the objects, and then discuss a few low-dimensional cases in full detail.